Accident as Unintended Events

An accident would require a mind in the first place, which had intent. So by saying that atheists believe everything is an accident is implying that atheists believe in a designer, who strayed from it's intent, which is clearly not the position of an atheist, by definition, who does not believe in the existence of any deities that had intent or made an accident.

If there are no gods, then our existence is neither accidental or intentional. It just is. We are the ones who are speculating on whether it's an acccident or intentional, which is irrelevant because from what we can tell, our existence is not the result of a sentient mind.

Accident as Improbable Events

Using the word "accident" implies that the phenomenon in question otherwise shouldn't happen. Thus, if the atheist believes it was an accident, then the atheist is foolishly believing that an event that shouldn't have happened, in fact did. If that's the case, the atheist could be accused of having faith, and thus, is a hypocrite.

The Third Option

Those who bring up this dichotomy are omitting a third option - "expected outcome". While an "accident" would be by definition an incredibly improbable event, an "expected outcome" would be by definition a highly probably event. That is, given a set of initial conditions, a particular outcome is to be reasonably and logically expected. Some examples would be:

If there's a lot of moisture in the air, and it's below freezing, it's to be expected that it would snow, and it's not an accident.

If there's open soil in an otherwise grassy field during the summer, it's to be expected that grass will start to grow in it, and it's not an accident.

Historical Example

After the Big Bang, a series of stages of the development of the universe lead until the present day. None of these stages are "accidents", but are all "expected outcomes":

Right after the Big Bang, we had a lot of elementary particles, such as quarks, floating around, and it's to be expected that they'd cool until they form sub-atomic particles, such as protons, electrons and neutrons.

After the hot protons, electrons and neutrons continue to cool, it is to be expected that they'd combine into hydrogen.

After some time of hydrogen and helium floating around the universe, it is to be expected that they'd fall into gravity wells, compress and ignite into stars.

As the nuclear fusion of the stars continues, it is to be expected that the process would build heavier atoms, such as nitrogen, carbon, oxygen, which alongside hydrogen, form the set of organic elements that are the building blocks to organic compounds.

As the star uses up its nuclear fuel, it is to be expected that the star will either nova or supernova, spreading the heavier elements around as stellar dust.

After some time of dust floating around, it is to be expected that it would fall into gravity wells, compress, and form planets and planetoids.

Etc.

Each step is logical and entirely reasonable to accept as true, especially is the claim is supported by evidence.